1. Field of the Invention
The present invention relates to the waiting time of telephone calls in inquiry centers, also called call centers or telephone-call response centers, and more particularly a distribution of calls to directory inquiry centers depending on the waiting time of the calls in them.
2. Description of the Prior Art
The U.S. Pat. No. 5,506,898 presents a method of estimating a waiting time in an inquiry center having several call queues as a function of priorities, so as to signal, by voice messaging, to each person requesting a call, the actual waiting time for obtaining an agent of the center.
If Q calls are already present in the queue, and if the inquiry center is dealing with one call on average every S seconds, the forecast waiting time AP is defined by AP=Qxc3x97S. The forecast waiting time AP is therefore the time which it would take for a call to go from the last place, in this instance the Qth place, to the first place in the queue.
The service duration perceived by the user is defined as being the average rate of progress in the queue, that is to say the time which it takes for a call to progress from one place to the next in the queue. The service duration perceived by the user is then updated upon each pick-up by an operator in the inquiry center, i.e. upon each response to a current call by the time which the current call has been on hold divided by the number of calls enqueued in the queue at the instant when the current call was parked in the queue. The service duration Sn perceived by the user is deduced from the following relationship according to the U.S. Pat. No. 5,506,898:
Sn=xcex2xc3x97Snxe2x88x921+(1xe2x88x92xcex2)xc3x97TAF. 
Snxe2x88x921 designates the service duration perceived by the user for the last call preceding the current call, and TAF designates the average rate of advance through the queue for the last call. xcex2 is a factor, typically 0.95, corresponding to a very heavy weighting of the irregularities in the service duration perceived by the user.
The reactivity to the change of the number of agents in the inquiry center is immediate according to the U.S. Pat. No. 5,506,898, since the staff numbers allocated to each group of queues are known. Consequently, the variations in the numbers of agents are reflected instantly on the service duration Sn perceived by the user by applying the multiplying factor
xcfx81=(new staff number)/(old staff number). 
The European patent application No. 772,335 describes a distribution of the calls in a system comprising several inquiry centers independent of one another. Each call is associated with a local inquiry center which should deal with the call in priority. If the local inquiry center is overloaded, calls which are associated with it can be directed to another, less heavily loaded, remote inquiry center.
The estimating of the load is based on the forecast waiting time AP described in the abovementioned U.S. patent.
For each incoming call, all the inquiry centers which offer the same skills are capable of being interrogated, via the telephone network, so as to compare their forecast waiting times and to determine the best queue for the call, i.e. the queue where the waiting time is the shortest.
The priority of the local inquiry center, by comparison with the other inquiry centers interrogated, is accentuated by adding a time quantum (constant) to the forecast waiting times of the remote centers by comparison with the forecast waiting time of the local center, for determination of the best queue.
However, in the case of a heavy load on the entire network, the time quantum is not sufficient, and the calls are no longer dealt with by their local inquiry centers without the service in them being enhanced.
The call distribution according to the abovementioned European patent application requires a dialog between the centers which interrogate each other in order to ascertain their forecast waiting times, because of the absence of a centralized processing facility between the inquiry centers. These interrogations take place upon each call, or periodically, so as to reduce the service traffic between the inquiry centers generated by these interrogations, and they therefore generate supplementary traffic between the centers.
The absence of centralization also poses problems of administration of the system of the inquiry centers and, in general, exhibits the drawbacks of the non-centralized solutions such as duplication of data, difficult administration and difficult upgrade of the center-management software.
The principal objective of the invention is to remedy the drawbacks of the methods according to the prior art set out above, and thus to concentrate the management of the calls of the inquiry centers and to reduce all supplementary traffic between the inquiry centers.
Accordingly, a method for distributing calls to directory inquiry centers, comprises a cycle of succeeding steps for a given inquiry center:
determining a forecast waiting time of the calls on the basis of a number of calls in waiting and of an estimated average waiting time per call in the given center,
routing the calls to the given center when the determined forecast waiting time is below a first threshold, and accepting calls from other inquiry centers the forecast waiting times of which are above the first threshold, when the determined forecast waiting time is below a third threshold,
routing the calls intended for the given center to another inquiry center on condition that the forecast waiting time in it is below the third threshold, when the determined forecast waiting time lies between the first threshold and a second threshold higher than the first threshold, and accepting calls from another inquiry center only if the forecast waiting time thereof is above the second threshold, when the determined forecast waiting time lies between the third threshold and a fourth threshold higher than the third threshold, and
routing calls intended for the given center to another inquiry center the forecast waiting time of which is below the fourth threshold, when the determined forecast waiting time is above the second threshold, and refusing all calls from other inquiry centers when the determined forecast waiting time is above the fourth threshold.
This latter step of routing and refusing guarantees that the given inquiry center, when it is saturated, no longer receives traffic from other centers and thus ensures the stability of the centers as a whole.
In practice, each inquiry center to which calls from the given center are routed is selected from a predetermined list of inquiry centers attributed to the given center. When each inquiry center has a forecast waiting time below the third threshold, it is found among the inquiry centers which are available by running cyclically through said predetermined list. According to another embodiment, when said each inquiry center has a forecast waiting time below the fourth threshold, it exhibits the shortest forecast waiting time of the list.
The method is less complex when the first and third thresholds are equal, and the second and fourth thresholds are equal.
In order to ensure better operating stability for all the inquiry centers, they do not instantaneously change state upon one of the four thresholds being crossed by the forecast waiting time. In respect, the crossing of each threshold in a given direction by the determined forecast waiting time in the course of the cycle increments a count, and the step of routing or of accepting or of refusing depending on this threshold is performed only when the count reaches a predetermined number during cycles preceding said cycle.
The invention also resolves another problem posed by the main object, because of the lack of knowledge of the number of agents present in each center, and thus of the average waiting time in each center, by any system for concentrating the management of the centers which is situated outside the centers themselves.
According to the invention, the forecast waiting time of the calls is equal to the product (Np+1)Sk*. Np denotes the number of calls placed in waiting in the given inquiry center which is incremented by one unity responsive to each call directed to the given center and which is decremented responsive to a pick-up for this call in the given center. Sk* denotes an estimated average waiting time between two pick-ups in the given center.
The average waiting time is estimated with the lack of knowledge of the number of agents in the given inquiry center. The estimated average waiting time Sk* is refreshed in response to the pick-up for each significant call in a queue in the given center according to the following relationship:
Sk*=xcex1Skxe2x88x921*+(1xe2x88x92xcex1)xcex94td. 
Skxe2x88x921* denotes the estimated average waiting time for a preceding significant call, xcex1 a smoothing factor, and xcex94td a difference between the instant of the pick-up for the significant call and the instant of the pick-up of the preceding call, whether it was or was not placed in waiting.
The smoothing factor is preferably determined as a function of the number of significant calls NAS per predetermined period, according to the formula:   α  =      0.1    NAS  
The invention concerns too a system for managing calls to directory inquiry centers. It is characterized in that it comprises a server which is linked to telephone exchange means serving the inquiry centers in order to receive call-processing signals from them, and which concentrates the management of the routing of the calls to the centers in accordance with the method of the invention. This concentration eliminates data exchanges between the inquiry centers and ensures better control for the operator of the inquiry centers as a whole. For example, the method of the invention may be implemented only during times of heavy traffic.